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A variable partitioning strategy for the multirate method in power systems

IEEE TRANSACTIONS ON POWER SYSTEMS 2008年第2期23卷 259-266页

作者： Chen, Jingjia Crow, Mariesa L. Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA

An application of the multirate method to differential and algebraic equations (DAEs) is discussed in this paper. Based on the specific formulation of the power systems algebraic equations, an effective algebraic variable partitioning strategy is developed and implemented. The application of the partitioning strategy to an example power system provides validation of the proposed partitioning strategy in terms of speed-up and accuracy.

关键词： differential and algebraic equations (DAEs) dynamic security assessment multirate method numerical integration power systems simulation

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A Posteriori analysis of a multirate numerical method for ordinary differential equations

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2012年 223卷 10-27页

作者： Estep, D. Ginting, V. Tavener, S. Colorado State Univ Dept Stat Ft Collins CO 80523 USA Univ Wyoming Dept Math Laramie WY 82071 USA Colorado State Univ Dept Math Ft Collins CO 80523 USA

In this paper, we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model. The main purpose of this paper is to present a hybrid a priori - a posteriori error analysis that accounts for the effects of projections between the coarse and fine scale discretizations, the use of only a finite number of iterations in the iterative solution of the discrete equations, the numerical error arising in the solution of each component, and the effects on stability arising from the multirate solution. The hybrid estimate has the form of a computable a posteriori leading order expression and a provably-higher order a priori expression. We support this estimate by an a priori convergence analysis. We present several examples illustrating the accuracy of multirate integration schemes and the accuracy of the a posteriori estimate. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Adjoint operator A posteriori estimates Discontinuous Galerkin method Iterative method multirate method Multiscale integration Operator decomposition

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A posteriori analysis of an iterative multi-discretization method for reaction-diffusion systems

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2013年 267卷 1-22页

作者： Chaudhry, J. H. Estep, D. Ginting, V. Tavener, S. Colorado State Univ Dept Math Ft Collins CO 80523 USA Colorado State Univ Dept Stat Ft Collins CO 80523 USA Univ Wyoming Dept Math Laramie WY 82071 USA

This paper is concerned with the accurate computational error estimation of numerical solutions of multi-scale, multi-physics systems of reaction-diffusion equations. Such systems can present significantly different temporal and spatial scales within the components of the model, indicating the use of independent discretizations for different components. However, multi-discretization can have significant effects on accuracy and stability. We perform an adjoint-based analysis to derive asymptotically accurate a posteriori error estimates for a user-defined quantity of interest. These estimates account for leading order contributions to the error arising from numerical solution of each component, an error due to incomplete iteration, an error due to linearization, and for errors arising due to the projection of solution components between different spatial meshes. Several numerical examples with various settings are given to demonstrate the performance of the error estimators. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Reaction-diffusion A posteriori estimates Discontinuous Galerkin method multirate method Multi-scale discretization Operator decomposition

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A cycle-based formulation for the simulation of multi time-scale systems - Application to the modeling of the storage system of a fully electric ferry

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MATHEMATICS AND COMPUTERS IN SIMULATION 2019年 158卷 403-417页

作者： Hmam, S. Olivier, J. -C. Bourguet, S. Loron, L. Bernard, N. Schaeffer, E. Univ Nantes IREENA 37 Blvd Univ St Nazaire France SERMA Ingn 5 Parc ArianeBlvd Chenes Guyancourt France

This paper addresses the simulation of complex systems which consider phenomena with different time scales. Such problems are encountered on studies of electrical systems which try to take into account the simulation of the power converter and its control laws, over representative operating cycles of several hours. Moreover, when storage elements are integrated into a power chain, their aging may need the designer to consider larger time scales, which can then exceed a few years. It is the reason why most studies separate the time scales between the slow dynamics for the energetic, thermal and aging phenomena, and the fast ones to study the power converter and its control laws. This paper presents an original cycle-based and multi-rate method for the simulation of power systems with a wide range of time scales and with high mutual dependency between the fast and slow state variables. This method is applied to the supercapacitor energy storage system of a full-electric ferry. The proposed simulation results take into account at the same time the switching of the power converter and the aging of the supercapacitor, with a reduction of the computational effort greater than 10(5). In other words, while a full calculation of the problem takes 10 centuries on a personal computer, the proposed method permits to have the same result in only 15 days. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： multirate method Computer simulation Supercapacitors Full-electric ferry Aging

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Model predictive control for cloud-integrated networked multiagent systems under bandwidth allocation

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INFORMATION SCIENCES 2019年 500卷 156-172页

作者： Yang, Hongjiu Ju, Shuang Zhang, Jinhui Yuan, Huanhuan Tianjin Univ Tianjin Key Lab Proc Measurement & Control Sch Elect & Informat Engn Tianjin 300072 Peoples R China Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Hebei Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

In this paper, a model predictive control (MPC) strategy is investigated for a cloud integrated networked multiagent system (NMAS) under bandwidth allocation. The cloud integrated NMAS is established in cloud computing and network environments. A Stackelberg game is exploited to describe the bandwidth allocation on the cloud-integrated NMAS. With effects on the bandwidth allocation, time delays are compensated by the MPC strategy which is based on a multirate method. Equilibrium solutions and stability conditions are given for the Stackelberg game and the cloud-integrated NMAS, respectively. Effectiveness of the proposed strategy is demonstrated by simulation results. (C) 2019 Published by Elsevier Inc.

关键词： Networked multiagent system Model predictive control multirate method Cloud computing Bandwidth allocation

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Efficient multirate simulation techniques for multi-physics systems with different time scales: application on an all-electric ferry design

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IET ELECTRICAL SYSTEMS IN TRANSPORTATION 2017年第1期7卷 23-31页

作者： Hmam, Sadok Olivier, Jean-Christophe Bourguet, Salvy Loron, Luc Univ Nantes IREENA St Nazaire France

This study introduces a multirate method for the simulation of multi-physics systems containing a wide range of time scales. This method has been designed for strongly coupled systems and is able to deal with high mutual dependency between fast and slow state variables. The proposed method based on a cycle formulation approach is applied to the ageing behaviour simulation of the energy storage unit (ESU) of an all-electric ferry. The objective is to design this ESU taking into account the electrical and thermal models, permitting to predict its ageing over the 20 years of the ferry operation. So, simulations could be excessively time consuming. The main objective behind this study is to reduce the simulation time to make possible an optimisation process. Using the proposed multirate method based on embedded extrapolation methods formulated on cycles, a speed-up factor of about 1000 compared with standard integration methods is obtained. Numerical results for the electric ferry example are presented for different tolerances in order to demonstrate the performance of the method.

关键词： multiphysics systems Transportation Marine transportation (energy utilisation) battery powered vehicles multirate method ageing energy storage all-electric ferry design ESU ageing behaviour simulation embedded extrapolation methods extrapolation Electrochemical conversion and storage Interpolation and function approximation (numerical analysis) multirate simulation techniques electrical models energy storage unit thermal models

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A decoupling method with different subdomain time steps for the nonstationary stokes-darcy model

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NUMERICAL methodS FOR PARTIAL DIFFERENTIAL EQUATIONS 2013年第2期29卷 549-583页

作者： Shan, Li Zheng, Haibiao Layton, William J. Xi An Jiao Tong Univ Coll Math & Stat Xian 710049 Peoples R China Univ Pittsburgh Dept Math Pittsburgh PA 15260 USA

This report analyzes a multirate, decoupling algorithm, which allows different time steps in the fluid region and the porous region for the nonstationary StokesDarcy problem. The method presented requires only one, uncoupled Stokes and Darcy subphysics and subdomain solve per time step. Under a time step restriction of the form Delta t <= C (physical parameters) we prove stability and convergence of the method. Numerical tests are given to show the convergence result and demonstrate the computational efficiency of the partitioned method. They also show that in the expected case of greater fluid velocities in the free-flow region than in the porous media region, allowing smaller time steps in the subregion with the faster velocities increases both accuracy and efficiency. (C) 2012 Wiley Periodicals, Inc. Numer methods Partial Differential Eq, 2013

关键词： asynchronous time stepping multirate method decoupling method Stokes-Darcy problem

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Simulation features of electric circuits with components described by discrete parameters

Simulation features of electric circuits with components des...

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International Conference on Modern Problems of Radio Engineering, Telecommunication and Computer Science

作者： Rendzinyak, Serhiy Korud, Andriy Lviv Polytech Natl Univ UA-79013 Lvov Ukraine

ISBN: (纸本)9781424413218

The problem of transient processes calculation in complex electric circuits consisting of elements with different physical nature using diakoptic approach is considered. Each element is presented as subsystem with its own mathematical model. Simulation of transient process is conducted using multirate method with estimation of interrelation between subcircuits in some time moments. Examples of calculation of linear and nonlinear circuit which contains long line are presented.

关键词： diakoptic multirate method subcircuit transient simulation long line

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Transient Analysis of High-Frequency Transmission Lines as Components of Heterogeneous Systems 14

Transient Analysis of High-Frequency Transmission Lines as C...

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14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET)

作者： Rendzinyak, Serhiy Korud, Vasyl Lviv Polytech Natl Univ Inst Power Engn & Control Syst Lvov Ukraine

ISBN: (纸本)9781538625569

The multirate method is used, which is based on a diakotic approach and which allows the most complete consideration of the features of each component for transient analysis of heterogeneous systems. An important aspect of the multirate method is the choice of the correction step and its timely change. The algorithm of simulation of dynamic regimes of heterogeneous electric circuits by the multirate method of integration of subsystems with lumped parameters and subsystems with distributed parameters is developed. The comparative analysis of the simulation of dynamic regimes of high-frequency long lines confirmed the effectiveness of the proposed algorithm for automatic selection of the step of matching the subcircuit solutions in the multirate method, which provided a reduction in the computational time in a stable computational process.

关键词： diakoptic multirate method subeireuit transient simulation transmission fine

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